The Ajax Coal Company is the only employer in its area. It can hire any number of female workers or male workers it wishes. The supply curve for women is given by

Lf = 100wf

MEf = Lf =50

and for men by

Lm = 9w2m

MEm = 1 / 2 √LM

Where wf and wm are, respectively, the hourly wage rate paid to female and male workers. Assume that Ajax sells its coal in a perfectly competitive market at $5 per ton and that each worker hired (both men and women) can mine two tons per hour. If the firm wishes to maximize profits, how many female and male workers should be hired and what will the wage rates for these two groups be? How much will Ajax earn in profits per hour on its mining machinery? How will that result compare to one in which Ajax was constrained (say, by market forces) to pay all workers the same wage based on the value of their marginal products?